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Large deviations for a binary collision model: energy evaporation 二元碰撞模型的大偏差：能量蒸发
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2021-11-24 DOI: 10.3934/mine.2023001
G. Basile, D. Benedetto, L. Bertini, E. Caglioti
{"title":"Large deviations for a binary collision model: energy evaporation","authors":"G. Basile, D. Benedetto, L. Bertini, E. Caglioti","doi":"10.3934/mine.2023001","DOIUrl":"https://doi.org/10.3934/mine.2023001","url":null,"abstract":"<abstract><p>We analyze the large deviations for a discrete energy Kac-like walk. In particular, we exhibit a path, with probability exponentially small in the number of particles, that looses energy.</p></abstract>","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42024083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Existence and nonexistence of traveling waves for the Gross-Pitaevskii equation in tori 环面Gross-Pitaevskii方程行波的存在性和不存在性
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2021-10-29 DOI: 10.3934/mine.2023011
F. S'anchez, D. Ruiz
{"title":"Existence and nonexistence of traveling waves for the Gross-Pitaevskii equation in tori","authors":"F. S'anchez, D. Ruiz","doi":"10.3934/mine.2023011","DOIUrl":"https://doi.org/10.3934/mine.2023011","url":null,"abstract":"In this paper we consider traveling waves for the Gross-Pitaevskii equation which are $ T $-periodic in each variable. We prove that if $ T $ is large enough, there exists a solution as a global minimizer of the corresponding action functional. In the subsonic case, we can use variational methods to prove the existence of a mountain-pass solution. Moreover, we show that for small $ T $ the problem admits only constant solutions.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41586738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Symmetry results for Serrin-type problems in ring-shaped domains 环状区域中serrin型问题的对称性结果
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2021-10-26 DOI: 10.3934/mine.2023027
S. Borghini
{"title":"Symmetry results for Serrin-type problems in ring-shaped domains","authors":"S. Borghini","doi":"10.3934/mine.2023027","DOIUrl":"https://doi.org/10.3934/mine.2023027","url":null,"abstract":"<abstract><p>In this work, we employ the technique developed in <sup>[<xref ref-type=\"bibr\" rid=\"b2\">2</xref>]</sup> to prove rotational symmetry for a class of Serrin-type problems for the standard Laplacian. We also discuss in some length how our strategy compares with the classical moving plane method.</p></abstract>","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41305935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Normal form for lower dimensional elliptic tori in Hamiltonian systems 哈密顿系统中低维椭圆环面的范式
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2021-10-19 DOI: 10.3934/mine.2022051
Chiara Caracciolo
{"title":"Normal form for lower dimensional elliptic tori in Hamiltonian systems","authors":"Chiara Caracciolo","doi":"10.3934/mine.2022051","DOIUrl":"https://doi.org/10.3934/mine.2022051","url":null,"abstract":"We give a proof of the convergence of an algorithm for the construction of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. The existence of such invariant tori is proved by leading the Hamiltonian to a suitable normal form. In particular, we adapt the procedure described in a previous work by Giorgilli and co-workers, where the construction was made so as to be used in the context of the planetary problem. We extend the proof of the convergence to the cases in which the two sets of frequencies, describing the motion along the torus and the transverse oscillations, have the same order of magnitude.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45616242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On symmetry of energy minimizing harmonic-type maps on cylindrical surfaces 关于柱面上能量最小化调和型映射的对称性
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2021-10-17 DOI: 10.3934/mine.2023056
G. Fratta, A. Fiorenza, V. Slastikov
{"title":"On symmetry of energy minimizing harmonic-type maps on cylindrical surfaces","authors":"G. Fratta, A. Fiorenza, V. Slastikov","doi":"10.3934/mine.2023056","DOIUrl":"https://doi.org/10.3934/mine.2023056","url":null,"abstract":"The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional in the class of $ mathbb{S}^2 $-valued maps defined in cylindrical surfaces. The model naturally arises as a curved thin-film limit in the theories of nematic liquid crystals and micromagnetics. We show that minimal configurations are $ z $-invariant and that energy minimizers in the class of weakly axially symmetric competitors are, in fact, axially symmetric. Our main result is a family of sharp Poincaré-type inequality on the circular cylinder, which allows for establishing a nearly complete picture of the energy landscape. The presence of symmetry-breaking phenomena is highlighted and discussed. Finally, we provide a complete characterization of in-plane minimizers, which typically appear in numerical simulations for reasons we explain.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45698335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Variational modeling of paperboard delamination under bending 弯曲作用下纸板分层的变分模型
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2021-10-16 DOI: 10.3934/mine.2023039
P. Dondl, S. Conti, J. Orlik
{"title":"Variational modeling of paperboard delamination under bending","authors":"P. Dondl, S. Conti, J. Orlik","doi":"10.3934/mine.2023039","DOIUrl":"https://doi.org/10.3934/mine.2023039","url":null,"abstract":"We develop and analyze a variational model for laminated paperboard. The model consists of a number of elastic sheets of a given thickness, which – at the expense of an energy per unit area – may delaminate. By providing an explicit construction for possible admissible deformations subject to boundary conditions that introduce a single bend, we discover a rich variety of energetic regimes. The regimes correspond to the experimentally observed: initial purely elastic response for small bending angle and the formation of a localized inelastic, delaminated hinge once the angle reaches a critical value. Our scaling upper bound then suggests the occurrence of several additional regimes as the angle increases. The upper bounds for the energy are partially matched by scaling lower bounds.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48619557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On fractional Schrödinger equations with Hartree type nonlinearities 关于具有Hartree型非线性的分数阶Schrödinger方程
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2021-10-14 DOI: 10.3934/mine.2022056
S. Cingolani, Marco Gallo, Kazunaga Tanaka
{"title":"On fractional Schrödinger equations with Hartree type nonlinearities","authors":"S. Cingolani, Marco Gallo, Kazunaga Tanaka","doi":"10.3934/mine.2022056","DOIUrl":"https://doi.org/10.3934/mine.2022056","url":null,"abstract":"<abstract><p>Goal of this paper is to study the following doubly nonlocal equation</p>\u0000\u0000<p><disp-formula>\u0000 <label/>\u0000 <tex-math id=\"FE1\">\u0000 begin{document}\u0000$(- Delta)^s u + mu u = (I_alpha*F(u))F'(u) quad {rm{in}};{mathbb{R}^N}qquadqquadqquadqquad ({rm{P}})\u0000$\u0000 end{document}\u0000 </tex-math>\u0000</disp-formula></p>\u0000\u0000<p>in the case of general nonlinearities $ F in C^1(mathbb{R}) $ of Berestycki-Lions type, when $ N geq 2 $ and $ mu > 0 $ is fixed. Here $ (-Delta)^s $, $ s in (0, 1) $, denotes the fractional Laplacian, while the Hartree-type term is given by convolution with the Riesz potential $ I_{alpha} $, $ alpha in (0, N) $. We prove existence of ground states of (P). Furthermore we obtain regularity and asymptotic decay of general solutions, extending some results contained in <sup>[<xref ref-type=\"bibr\" rid=\"b23\">23</xref>,<xref ref-type=\"bibr\" rid=\"b61\">61</xref>]</sup>.</p></abstract>","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46135257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
A Hong-Krahn-Szegö inequality for mixed local and nonlocal operators 混合局部和非局部算子的一个Hong Krahn-Szegö不等式
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2021-10-14 DOI: 10.3934/mine.2023014
Stefano Biagi, S. Dipierro, E. Valdinoci, E. Vecchi
{"title":"A Hong-Krahn-Szegö inequality for mixed local and nonlocal operators","authors":"Stefano Biagi, S. Dipierro, E. Valdinoci, E. Vecchi","doi":"10.3934/mine.2023014","DOIUrl":"https://doi.org/10.3934/mine.2023014","url":null,"abstract":"Given a bounded open set $ Omegasubseteq{mathbb{R}}^n $, we consider the eigenvalue problem for a nonlinear mixed local/nonlocal operator with vanishing conditions in the complement of $ Omega $. We prove that the second eigenvalue $ lambda_2(Omega) $ is always strictly larger than the first eigenvalue $ lambda_1(B) $ of a ball $ B $ with volume half of that of $ Omega $. This bound is proven to be sharp, by comparing to the limit case in which $ Omega $ consists of two equal balls far from each other. More precisely, differently from the local case, an optimal shape for the second eigenvalue problem does not exist, but a minimizing sequence is given by the union of two disjoint balls of half volume whose mutual distance tends to infinity.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46067236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 26
Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations Ito随机微分方程的渐近对称性和渐近解
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2021-10-01 DOI: 10.3934/mine.2022038
G. Gaeta, R. Kozlov, Francesco Spadaro
{"title":"Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations","authors":"G. Gaeta, R. Kozlov, Francesco Spadaro","doi":"10.3934/mine.2022038","DOIUrl":"https://doi.org/10.3934/mine.2022038","url":null,"abstract":"We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the deterministic one, such as conditional, partial and asymptotic symmetries. A number of explicit examples are presented.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43243818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
On the influence of gravity in the dynamics of geophysical flows 地球物理流动动力学中重力的影响
IF 1 4区 工程技术
Mathematics in Engineering Pub Date : 2021-09-20 DOI: 10.3934/mine.2023008
D. Santo, F. Fanelli, Gabriele Sbaiz, Aneta Wr'oblewska-Kami'nska
{"title":"On the influence of gravity in the dynamics of geophysical flows","authors":"D. Santo, F. Fanelli, Gabriele Sbaiz, Aneta Wr'oblewska-Kami'nska","doi":"10.3934/mine.2023008","DOIUrl":"https://doi.org/10.3934/mine.2023008","url":null,"abstract":"In the present paper, we study a multiscale limit for the barotropic Navier-Stokes system with Coriolis and gravitational forces, for vanishing values of the Mach, Rossby and Froude numbers ($ {rm{Ma}} $, $ {rm{Ro}} $ and $ {rm{Fr}} $, respectively). The focus here is on the effects of gravity: albeit remaining in a low stratification regime $ {rm{Ma}}/{rm{Fr}}, rightarrow, 0 $, we consider scaling for the Froude number which go beyond the \"critical\" value $ {rm{Fr, = , sqrt{rm{Ma}}}} $. The rigorous derivation of suitable limiting systems for the various choices of the scaling is shown by means of a compensated compactness argument. Exploiting the precise structure of the gravitational force is the key to get the convergence.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44747753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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